Results from the occultation of the sun by Neptune imply a temperature of 750 +/- 150 kelvins in the upper levels of the atmosphere (composed mostly of atomic and molecular hydrogen) and define the distributions of methane, acetylene, and ethane at lower levels. The ultraviolet spectrum of the sunlit atmosphere of Neptune resembles the spectra of the Jupiter, Saturn, and Uranus atmospheres in that it is dominated by the emissions of H Lyman alpha (340 +/- 20 rayleighs) and molecular hydrogen. The extreme ultraviolet emissions in the range from 800 to 1100 angstroms at the four planets visited by Voyager scale approximately as the inverse square of their heliocentric distances. Weak auroral emissions have been tentatively identified on the night side of Neptune. Airglow and occultation observations of Triton's atmosphere show that it is composed mainly of molecular nitrogen, with a trace of methane near the surface. The temperature of Triton's upper atmosphere is 95 +/- 5 kelvins, and the surface pressure is roughly 14 microbars.